So I've decided to skip the week and postpone to next week, so he doesn't feel excluded. He however suggested we may also find another player so if someone cannot make it the others can still play: well, this line made me suspicious. What was he implying?
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How should I approach this? Do I start searching for a 4th player as he himself suggested, or would that make him feel like I am replacing him?
People on the internet will not know what he meant. We cannot read his mind.
To first approximation, take people at their word - he suggested you find another player. If he isn't actually okay with that, that's his own darned fault. If he wasn't telling the truth, or was playing passive-aggressive games, he gets what that behavior earns you.
However, as others have said - when in doubt, ASK. Talk to each other like mature adults.
Note that as the world opens up, there's currently a shortage of workers - that means that a lot of people are changing jobs, and this is very true in the software world. The teams your player works with may have lost members, but still have to meet deadlines, and may just be too busy.
The flip side of this is that "for work reasons" is a solid go-to when the person doesn't want to tell you why. And, in a practical sense... that's okay. Giving a reason is nice, but not required.